Ὅταν δὲ ἔλθῃ ὁ υἱὸς τοῦ ἀνθρώπου ἐν τῇ δόξῃ αὐτοῦ καὶ πάντες οἱ ἄγγελοι μετ᾿ αὐτοῦ, τότε καθίσει ἐπὶ θρόνου δόξης αὐτοῦ· (NA28)
But when the son of man comes in his glory (doxē autou) and all the angels with him, then he will sit on the throne of his glory (doxēs autou). (Susan's wooden rendition)
There is no distinction drawn here between two types of glory. It's exactly the same phrase.
The NIV 1984, quoted in the question, has translated them differently because the latter is a juxtaposition of two nouns – thronou (throne) and doxēs (glory) – and the second is in the genitive case (i.e. “throne of glory”). This can be construed as an attributive (a.k.a. Hebrew) genitive. In this construction, the second noun carries an adjectival idea and modifies the first. It is especially common with abstract nouns like doxa.
When an attributive genitive is understood (as most translations do here), sometimes we can get away with translating it into English as 'x of y', mimicking the Greek syntax. (See, e.g., Rom 6:6, commonly rendered 'body of sin', but also = 'sinful body'.)
Here, arguably we could get away with this (so KJV, RSV, NRSV, etc.), but the NIV translators evidently thought this wasn’t adequately fluent (or perhaps transparent) English. To smooth it out, the basic process is:
Make the genitive into an explicit English attributive (i.e. adjective): throne of his glory → glorious throne (so ESV, NIV ,2 NET, NKJV, etc.), +/-
Provide an interpretation of what the translators think “glorious” means in this context. Adjectives such as majestic (CEB), royal (CEV), and great (ICB) are used in other translations to modify “throne”.
The NIV 1984 (but not 2011) appears to have followed both of these steps to generate the adjective “Heavenly”. Oddly, though, they create an adverbial phrase and have doxēs doing “double duty” meaning both “Heavenly” and “glory”. I see no other translation that does this. Genitives can occasionally be adverbial, but juxtaposed with another noun like this it is not the most natural translation. Even if it were adverbial, there remains an extraneous word+concept here.
This seems to be an idiosyncrasy of the NIV 1984 that has, understandably, created the confusion expressed in the question.2 The NIV 2011 and other translations that use an English adjective have made a rational translation decision, but the more dynamic versions obscure the consistent use of doxa autou (his glory).
1. Oddly, “glorious throne” is used by NIV 1984 in Matt. 19:28, translating the same Greek phrase as 25:31. In the 2011 edition, both are rendered “glorious throne”.
2. I would love to be corrected if somebody can explain this!